Another discussion with a friend

A workmate and I have on-going disc^H^H^H^H arguments about Physics and I need a third party to break the deadlock on the latest one. I hope you guys can help.

He is of the opinion that the effect on a car driver of running into a brick wall at 60mph is the same as if he had a head-on collision with another car heading at 60mph in the other direction. His theory is based on the fact that the force needed to bring each vehicle to a stop is the same in both cases, using F=m.a.

I just can't believe that to be the case. As far as I'm concerned having a head-on with another car where both are travelling at 60mph is equivalent to hitting a wall at 120mph and so the effects would be doubled. This is based on kinetic energy being equal to 1/2.m.v(squared), in which case with a relative speed of 120mph, rather than 60mph with the wall, the kinetic energy of the system is quadrupled. Assuming that the kinetic energy is dissipated only through the cars in both case (i.e. the wall absorbs nothing) this would mean that the energy dissipated through the two cars would need to be doubled in order to bring the kinetic energy of the system to zero and having everything end up stationary.

I put the question to other non-Physics people and I have a 50/50 split supporting each theory so I'm hoping that you guys with a good amount of Physics knowledge will be able to explain it well enough to put it to rest. I'm quite prepared to be proven wrong so fire away

If the brick wall is really hard, then your friend is right. You can think of the brick wall as a "mirror": leaving it out, and "symmetrising" the setup will not change the solution on one side of the symmetry line.
It's a bit like having charges distributed over a conducting plane: the field is the same as when you put mirror charges on the other side and remove the plane.

EDIT: try first thinking of colliding marbles. When you hit a wall with a marble, and it undergoes an elastic collision, you have the same kinetics as when two marbles hit eachother at equal but opposite speed.

As to your energy argument, this is not correct. Two cars speeding at 60mph have a global kinetic energy which is ~ 60^2 + 60^2 = 2 x 60^2. But this kinetic energy is to be distributed over two cars to crumple them, so the energy available to each car to crumple is ~ 60^2.
One car speeding towards a wall has total energy of ~60^2, totally dissipated into the crumpling of one car.

Someone should hunt through PF postings and find out all the threads that are identical to the OP here. I am beginning to be very skeptical that there is a "discussion" going on, because almost all of the posts on this seem to have rather uncanny identical premise with almost the same parameters.